Problem: Simplify the following expression: $t = \dfrac{5q^2 + 25q - 120}{q + 8} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ t =\dfrac{5(q^2 + 5q - 24)}{q + 8} $ Then we factor the remaining polynomial: $q^2 + {5}q {-24} $ ${8} {-3} = {5}$ ${8} \times {-3} = {-24}$ $ (q + {8}) (q {-3}) $ This gives us a factored expression: $\dfrac{5(q + {8}) (q {-3})}{q + 8}$ We can divide the numerator and denominator by $(q - 8)$ on condition that $q \neq -8$ Therefore $t = 5(q - 3); q \neq -8$